Two-Grid Finite Volume Element Methods for Solving Cahn–Hilliard Equation

This paper proposes a two-grid mixed finite volume element method (TGMFVE) that uses a θ time discrete scheme to solve the Cahn–Hilliard equation. This method is separated into two steps. In the first step, the solution of the Cahn–Hilliard equation can be obtained by using a mixed θ scheme of the finite volume element method on a coarse grid using an iterative algorithm. The second step involves using the linearized mixed θ scheme finite volume element method to solve the equation on a fine grid. The stability analysis of the θ scheme of the two-grid mixed finite volume element method has been performed. The priori error estimation for L2 norm and H1 norm is also analyzed. The results of theoretical analysis are confirmed by numerical experiments. The results show that the theoretical results match the actual numerical results.